Hex Empire unfortunately, is not about an ancient land of witches turning each other into mules and spiders. The name refers to hexagons, the traditional battleground of the pen-and-paper wargamer. Hexagons tile well, you see, and they look nice with doodles of rivers and mountain ranges between them. They are pointy, but not so much that you need to wear goggles while working with them, like you do with squares or triangles.
It's explaind during the game. But you use both Mouse and Keyboard buttons.
Your objective is to capture the capital cities of your enemies.
The map is littered with smaller cities and coastal ports, and generally speaking, it is a good idea to control as many of these as possible.
At the end of each turn, each city in your territory will generate a unit 10 soldiers strong, while ports and the rest of your occupied land add soldiers to your cities randomly.